Can I use gmail to check and send email from an email account I have here?

Definitely! In many cases, we actually would recommend you do this, in order to avoid filling up your hosting account’s space with emails. You can create an email address on your hosting account, and instead of forwarding mail, you can just tell Gmail to check and send through that account. This keeps your hosting space cleared out, and lets you still use your domain for your email (instead of a generic @gmail.com address.)